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Course Criteria
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4.00 Credits
Prerequisite: At least a C- or better in MA252. A continua- tion of MA252 into multivariable calculus. Topics include vectors, lines, planes, and surfaces in three dimensions; vector functions and their derivatives and integrals; partial derivatives, gradients, directional derivatives, maxima, minima, Lagrange multipliers; multiple inte- grals, area, volume, surface area, integration in differ- ent coordinate systems. Line integrals, Green's theorem, Stokes' theorem and the divergence theorem are also studied. (Fall only)
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3.00 Credits
Prerequisite: MA252. The logic of compound statements, sequences and mathematical induction, set theory, counting arguments, recurrence relations, permuta- tions, combinations and probability. Applications may include analysis of algorithms and shortest path prob- lems. Problem solving is stressed. (Fall only)
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3.00 Credits
Prerequisite: MA395. A rigorous development of topics in calculus, and a systematic study of basic analysis with an emphasis on formal proofs. Topics include properties of the real line, sequences, series, theory of limits,213 continuity, theory of differentiation, and integration of functions of one variable. (Fall only)
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3.00 Credits
Prerequisite: MA351, MA421. A continuation of MA421. Possible topics include theory of integration of functions of one variable, improper integrals, series, functions of several variables, and metric spaces. (Spring only, Even Years)
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3.00 Credits
Prerequisite: MA421 or written permission of the instructor. Geometry of complex numbers, complex functions, analytic functions, harmonic functions, contour integra- tion, Cauchy's Integral Formula, Laurent series, residue theory, conformal mappings. (Spring only, Odd Years)
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3.00 Credits
Prerequisite: MA301, MA302, MA351, or written permission of the instructor. Floating point arithmetic, rounding errors, root-finding, interpolation and approximation, numeri- cal integration. Additional topics covered may include solutions of ordinary differential equations, direct and iterative solutions of linear systems, optimization, nonlin- ear systems of equations. (Spring only, Even Years)
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3.00 Credits
Prerequisite: MA252. A review of Euclidean geometry and an introduction to non-Euclidean geometry. Rig- orous deduction and axiom systems are emphasized. Possible techniques include the use of coordinate geometry, linear algebra, and computer geometry sys- tems. (Spring only, Even Years)
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3.00 Credits
Prerequisite: MA301, MA395. An investigation of the fundamental algebraic systems of groups, rings, and fields. Homomorphisms, cosets, Lagrange's theorem, quotient structures, and symmetry groups. (Fall only)
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3.00 Credits
Prerequisite: MA441. A continuation of MA441. Topics drawn from Sylow theory, ring theory, Galois theory, field extensions, and finite fields. May include applica- tions from combinatorics, computing and coding. (Spring only, Odd Years)
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3.00 Credits
Prerequisite: MA301. A deeper study of matrices and their applications, diagonalization, canonical forms, eigen- vectors and eigenvalues, perturbation of matrices, computational algorithms. (Fall only, Even Years)
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